Answer:
a)
For this case we can use the normal standard table or excel and the complement rule and we got:
b)
For this case we can use the normal standard table or excel and we got:
c)
And we can find this probability with this difference:
Step-by-step explanation:
Previous concepts
Normal distribution, is a "probability distribution that is symmetric about the mean, showing that data near the mean are more frequent in occurrence than data far from the mean".
The Z-score is "a numerical measurement used in statistics of a value's relationship to the mean (average) of a group of values, measured in terms of standard deviations from the mean".
Part a
Let Z the random variable that represent the bone density scores of a population, and for this case we know the distribution for X is given by:
Where and
We are interested on this probability
For this case we can use the normal standard table or excel and the complement rule and we got:
Part b
We are interested on this probability
For this case we can use the normal standard table or excel and we got:
Part c: not significant (or less than 2 standard deviations away from the mean).
For this case we want this probability:
And we can find this probability with this difference: